Questions and Answers
What is the sum of the interior angles in a convex quadrilateral?
Which of the following are properties of a parallelogram? (Select all that apply)
In a rhombus, all sides are congruent.
True
What is a rectangle?
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What defines a square?
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If a figure has two pairs of consecutive sides congruent, what can be inferred about it?
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If a quadrilateral has one pair of opposite sides that are congruent and parallel, what can be inferred?
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What do the diagonals of a parallelogram do?
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If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a rectangle.
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What defines a trapezoid?
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A polygon with four sides is called a ______.
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What is the relationship between the opposite angles of a parallelogram?
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In which type of quadrilateral are the diagonals always perpendicular?
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In an isosceles trapezoid, the non-parallel sides are congruent.
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Match the following quadrilaterals with their definitions:
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What can be inferred if the opposite sides of a quadrilateral are congruent?
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Study Notes
Properties of Quadrilaterals
- The sum of interior angles in a convex quadrilateral is 360 degrees.
- The sum of exterior angles in a convex quadrilateral is also 360 degrees.
Properties of Specific Quadrilaterals
- Parallelogram: Opposite sides and angles are congruent, consecutive angles are supplementary, diagonals bisect each other.
- Rhombus: All sides are congruent, opposite angles are congruent, diagonals bisect each angle and are perpendicular to each other.
- Rectangle: All angles are right angles, diagonals are congruent and bisect each other, opposite sides are parallel and congruent.
- Square: Combines properties of both rhombus and rectangle; all sides are congruent, all angles are right angles, diagonals bisect opposite angles and are congruent.
- Kite: One diagonal bisects two angles, diagonals are perpendicular, has two pairs of consecutive sides that are congruent, and one pair of opposite angles congruent.
- Trapezoid: Has exactly one pair of opposite parallel sides.
- Isosceles Trapezoid: One pair of opposite parallel sides, the non-parallel sides are congruent, and both pairs of base angles are congruent.
Conditions for Parallelograms
- If a quadrilateral has opposite sides that are congruent, then it is a parallelogram.
- If both pairs of opposite angles are congruent, it indicates a parallelogram.
- If the diagonals bisect each other within a quadrilateral, it is classified as a parallelogram.
- A quadrilateral with one pair of opposite sides that are both congruent and parallel is a parallelogram.
- If each pair of consecutive angles in a quadrilateral is supplementary, it also qualifies as a parallelogram.
Specific Implications of Quadrilateral Types
- A rhombus is specifically an equilateral parallelogram with perpendicular diagonals.
- A rectangle is an equilangular parallelogram characterized by congruent diagonals.
- A square is a unique case of both a rectangle and a rhombus, exhibiting all respective properties.
Symmetry and Diagonal Properties
- Diagonals of a rectangle are congruent; it has two lines of symmetry.
- Diagonals of a rhombus are perpendicular; the rhombus also has two lines of symmetry.
- In a square, the diagonals are both perpendicular and congruent.
General Definitions
- Quadrilateral: A polygon with four sides.
- Parallelogram: A quadrilateral where both pairs of opposite sides are parallel.
- Rhombus: A parallelogram with four congruent sides.
- Rectangle: A parallelogram with four right angles.
- Square: A parallelogram with four congruent sides and angles.
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Description
Test your knowledge on the properties of various quadrilaterals including parallelograms, rhombuses, rectangles, squares, kites, and trapezoids. This quiz will help you understand the essential characteristics and relationships between these geometric shapes.
